Archive for September, 2015

Daily Report 28/9/15

There were 3154 files downloaded or hits from 471 reading sessions or distinct visits, 1.36 gigabytes downloaded during the day from private site extensive downloads. Main spiders baidu, google, MSN, yandex and yahoo. F3(Sp) 803, Collected ECE2 papers 732, Collected Evans / Morris papers 560 (est), Collected Scientometrics 546, Barddoniaeth / Collected Poetry 378, Autobiography Volumes One and Two 367, Proofs that no torsion means no curvature 220, Principles of ECE 195, Eckardt / Lindstrom papers 180, Engineering Model 168, UFT88 120, Evans Equations 113 (numerous Spanish), CEFE 79, UFT311 78, UFT321 78, Llais 45, UFT313 50, UFT314 38, UFT315 45, UFT316 49, UFT317 54, UFT318 56, UFT319 63, UFT320 47, UFT322 57, UFT323 47, UFT324 72, UFT325 75, UFT326 65, UFT327 14 to date in September 2015. Institute of Physics University of Sao Paolo Brazil UFT149(Sp); Pontifical Bolivarian University Colombia Antisymmetric Connection and refutation of Einsteinian GR (Sp); geology University of Oviedo Spain F1(Sp); Dragana Campus Dimokritio University Thrace Greece Essay 24 Derivation of the Pauli Exclusion Principle from the Fermion Equation; Italian National Institute for Nuclear Physics (INFN), Southern National Laboratory at Catania LCR resonant; Utrecht University Netherlands general. Intense interest all sectors, updated usage file attached for September 2015.

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Sommerfeld and Dirac Atoms

The numerical methods and results for the special relativistic orbit can be used to solve for the Sommerfeld atom (1913) and Dirac atom (1927 / 1928) without the use of the crude approximations used by Dirac. He made these for the sake of analytical tractability, and they are very rough, the total energy is approximated by the rest energy for example, and it is assumed that U << m c squared. The Dirac equation has been improved into the ECE fermion equation by the AIAS group, removing negative energy and the unobservable Dirac sea. I will proceed to write up my sections of UFT328, and UFT329 will probably deal with the Sommerfeld and Dirac hamiltonians and lagrangians. The former use O(3), the latter use SU(2) and the Pauli matrices, otherwise they are the same before quantization. The early quantization by Bohr and Sommerfeld (1912 to 1913) was replaced by Schroedinger quantization in the early twenties, and that was used by Dirac. They are both theories of special relativistic quantum mechanics. In ECE2, special relativity in one sense is also generally covariant, so the distinction between special and general relativity is no longer needed. The physics all becomes Cartan geometry. The true Sommerfeld orbitals are the quantized versions of the ones that appear in the following postings on this blog, with the gravitational potential between a mass m in orbit around a mass M replaced by the electrostatic potential between proton and electron in the H atom.

The dr / dtheta Comparison

This is a particularly interesting and important result, the graphics here vividly illustrate the effect of special relativity. The overall conclusion is the Lorentz covariant ECE2 theory allows the use of the familiar equations of special relativity, notably the hamiltonian and lagrangian. A numerical method of solution developed by co author Horst Eckardt leads to results that cannot be obtained analytically. This situation is similar to molecular dynamics or Monte Carlo computer simulation, where results can be obtained that are intractable analytically. So the numerical solution of the lagrangian of special relativty produces the true orbit. This method also produces the true orbitals of the Sommerfeld atom, the first relativistic quantum theory. The Einstein theory produces a ridiculously incorrect orbit if we expand our horizons form the seconds of arc perspective to the complete orbit. The Marion / Thornton approximation to Einstein gives a completely unphysical orbit that diverges. The x theory produces a precessing ellipse initially, but as x increases the orbit of x theory becomes the fractal conical sections, also discovered by the AIAS group. The fractal conical sections are mathematically valid, but they do not give the true orbit. So mainframes and supercomputers should be used to try to give a precise comparison of special relativistic precession with experimental data. Given the new principle of special relativity of recent UFT papers that v0 squared is bounded above by c squared / 2, special relativity gives light deflection by gravitation exactly. So these are historic advances in physics and cosmology. Special relativity also describes the fundamentals of the velocity curve of a whirlpool galaxy, where Einstein fails completely. So I will now proceed to write up UFT328, Sections One and Two.

To: Emyrone@aol.com
Sent: 28/09/2015 21:41:51 GMT Daylight Time
Subj: PS PS: p/L and other quantities in relativistic context

PS PS: I forgot the dr/dtheta comparison. It can be seen that this
changes sign, therefor the doubled structures. In polar diagrams,
negative functional values are represented by an argumen t schift of 180
degrees.
Horst

Am 28.09.2015 um 22:32 schrieb Horst Eckardt:
> PS: it makes less sense to compare orbital radii between different
> theories directly because precession leads to large differences. You
> would have to subract the precession anyhow to make differences in
> orbital curvature comparable for example.
>
>
> Am 28.09.2015 um 22:28 schrieb Horst Eckardt:
>> I compared the results of the Newtonian Lagrange eqautions with those
>> of the relativistic Lagrangian. Initital conditions were the same,
>> and angular momenta were also the same. It is not possible to use L0
>> in the relativistic equation because this is not a constant of motion
>> there.
>> From Fig.7 (orbits) it can be seen that the relativistic orbit is
>> significantly larger for the same intial conditions. This is a hint
>> that it makes no sense to use an equation for the non-relativistic
>> orbit (p0 in note 328(5)) in a relativistic context.
>> Fig. 10 shows gamma(theta), this varies only between 1.00 and 1.03.
>> However the orbital precession is significant, see Fig. 7. The
>> quantities rdot, theta dot, v/c resemble each other, there is a bend
>> at the aphelion. This also holds for p/L (Fig. 13).
>> I will see which anlaytical results can be compared with these
>> curves, for example extracting a precession parameter.
>>
>> Horst
>

Graphical Results for Orbital Precession in Special Relativity

These are excellent results and graphics, proving conclusively that special relativity can produce orbital precession. So orbital precession is not a conclusive test of Einsteinian general relativity, because it can be produced by special relativity. It is also known that Einstein’s mathematics are riddled with errors which are well known and can no longer be just ignored. To do that is unscientitic.These are major advances as can be seen from the intense interest in the latest UFT papers. I think that the best way forward is to use (p / L) squared and gamma from these computer results in Eq. (14) of Note 328(5). It is very interesting to see the difference between the relativistic and classical p / L. The orbital precession is very clear from these results. Also the graphs of r dot and theta dot are important and interesting.

To: Emyrone@aol.com
Sent: 28/09/2015 21:29:03 GMT Daylight Time
Subj: p/L and other quantities in relativistic context

I compared the results of the Newtonian Lagrange eqautions with those of
the relativistic Lagrangian. Initital conditions were the same, and
angular momenta were also the same. It is not possible to use L0 in the
relativistic equation because this is not a constant of motion there.
From Fig.7 (orbits) it can be seen that the relativistic orbit is
significantly larger for the same intial conditions. This is a hint that
it makes no sense to use an equation for the non-relativistic orbit (p0
in note 328(5)) in a relativistic context.
Fig. 10 shows gamma(theta), this varies only between 1.00 and 1.03.
However the orbital precession is significant, see Fig. 7. The
quantities rdot, theta dot, v/c resemble each other, there is a bend at
the aphelion. This also holds for p/L (Fig. 13).
I will see which anlaytical results can be compared with these curves,
for example extracting a precession parameter.

Horst

Discussion of Note 328(4), Part Three

Many thanks, a very useful check by computer. .

To: EMyrone@aol.com
Sent: 28/09/2015 15:40:13 GMT Daylight Time
Subj: Re: Discussion of Note 328(4)

you are right, the term is correct. The computer gives a simplified expression without double fractions, see last two formulas.

Horst

Am 28.09.2015 um 10:13 schrieb EMyrone:

Thanks again.

1) Can you run this through the computer? If the rightmost term does not contain r, the dimensionality is wrong, because eps r / alpha is dimensionless.
2) Agreed.
3) Agreed.

To: EMyrone
Sent: 27/09/2015 20:49:28 GMT Daylight Time
Subj: Re: 328(4): More Accurate Theory of Orbital Precession in Special Relativity

In eq.(15) the right-most squared term should not contain “r”.
in (29) sin theta should be repaced by sin (gamma theta).
In (39) the second row has probably to have 1+epsilon in the denominator, not 1+alpha.

Horst

Am 26.09.2015 um 14:48 schrieb EMyrone:

This note defines the precessing orbit as Eq. (15), so the ratio p / L can be calculated using Eqs. (15) and (17). This ratio can be compared with p / L from the lagrangian of special relativity Eq. (18) with gravitational potential (19), and can be compared with p / L from other theories, for example the x theory or the general precessing orbit (22). Finally, using the orbit (26), with x = gamma, the orbit (9) of special relativity can be deduced. So special relativity can be thought of as x theory with x = gamma, the Lorentz factor. This gives the precession (34), and delta theta can be calculated to be Eq. (44). At the perihelion Eq. (45) applies. In the next note 328(5) the ratio p / L will be calculated analytically by approximating the relativistic lagrangian theory, which leads to the relativistic Leibnitz equation of orbits and the definition of the relativistic angular momentum as a constant of motion. Knowing p / L analytically gives d theta / dr and the true orbit of specail relativity. The ratio p / L was computed by a scatter plot method by co author Horst Eckardt in UFT324 and UFT325.

328(4).pdf

Daily Report Sunday 27/9/15

There were 2863 hits or files downloaded from 349 distinct visits or reading sessions, main spiders baidu, google, MSN and yahoo. F3(Sp) 786, Collected ECE2 papers 698, Evans / Morris papers 540(est), Collected Scientometrics 528, Autobiography volumes one and two 357, Barddoniaeth / Collected Poetry 351, Proofs that no torsion means no gravitation 214, Principles of ECE 183, Eckardt / Lindstrom papers 169, Engineering Model 166, UFT88 117, Evans Equations 109 (numerous Spanish), UFT311 77, CEFE 76, UFT321 75, UFT313 48, UFT314 37, UFT315 44, UFT316 46, UFT317 51, UFT318 55, UFT319 62, UFT320 44, UFT322 53, UFT323 42, UFT324 70, UFT325 71, UFT326 64, UFT327 11, Llais 44 to date in September 2015. McMaster University Canada UFT25; Lacompany France extensive download; Bose Institute India UFT33. Intense interest all sectors, updated usage file attached for September 2015.

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328(5): The Exact Orbit of Special Relativity

This is given by Eq. (22), whose right hand side can be worked out completely in terms of r and compared with the classical result (19). It can also be compared with x theory of a precessing ellipse, Eq. (25), and with the general precessing ellipse, Eq. (27). It is known from the numerical work of UFT324 and UFT325 by Horst Eckardt that the orbit of special relativity precesses. Eq. (22) is also the exact solution for the Sommerfeld atom before quantization. It is also known that this solution of the Sommerfeld atom is a precessing ellipse. The method used is start with the well known hamiltonian of general relativity, Eq. (1), and to prove that the transition from classical orbits to special relativistic orbits is given by Eq. (12). This is an entirely new result.

a328thpapernotes5.pdf